Applying engineering principles to exercise

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Most individuals, athletes or not, have experienced a musculoskeletal injury due to the overuse of a specific tissue or muscle. These overuse injuries can slow down an individual either in the workout routines or daily life. While not all injuries react the same way, many overuse injury areas are known to build up lymphatic fluid causing swelling and pain. The swelling and pain come from the accumulated lymphatic fluid putting increased pressure on the injured muscle or tissue.

Taping using Kinesio Tape (KT) has become a very popular proposed treatment and recovery aid over the past couple of years. KT became popular after the 2008 Beijing Olympic games, where beach volleyball player Kerri Walsh Jennings caught the attention of many spectators for wearing multi colored tape strips on her shoulder. KT is believed to lift the skin from the underlying layers of fascia, or bands or connective tissue. The lifting of the skin from the fascia results in a greater movement of lymphatic fluid, which transports white blood cells throughout the body and removes bacteria, waste products, and cellular debris. When the tape is correctly used it may also be able to provide support to the surrounding muscles and help to ensure that the muscle does not over extend or over contract [1].

Figure 1. Athlete wearing Kinesio Tape.

Research suggests show that the tape will allow increased oxygen to the injured muscle and decreased inflammation. A 2012 study tested the effects of KT on blood flow in the gastrocnemius muscle and whether or not the way KT is applied changes the outcome on the muscle performance. In this study 61 healthy active individuals with no recent leg injuries were assigned to either treatment KT, sham KT, or a control group. Before taping a blood flow, circumference, and water displacement was taken for the gastrocnemius muscle. The individuals were then taped, and each measurement was taken again 24 hours and 72 hours after being taped. The results of this study showed no significant differences in the blood flow to the muscle using KT. There was also no change in the muscle’s performance based on the application technique of the tape [1].

From five previous systematic reviews, a new systematic review had been created to evaluate whether or not KT was more effective than no treatment or a placebo treatment, for people with musculoskeletal conditions, on pain levels, disability, and quality of life. Several different studies had been performed that looked at the pain levels on a scale from (0-10) for performing different activities while wearing either KT or another form of tape. These studies are prone too potential bias from the users and small sample sizes. Many of the referenced studies only shared certain of the results or were considered significant but of low quality [2].

Within a study done on subjects who had been diagnosed with rotator cuff tendonitis/impingement similar results were found as in the studies before. The only difference in this study was that they took self-reported measurement for range of motion along with pain. While the taping was ineffective compared to sham tape in long term, the KT provide immediate in pain free abduction range of motion. Once again, this study was limited to a. young population and it lacked a control group for comparison [3].

Although studies show that KT is ineffective in aiding injury rehabilitation, it is. Still used often by many groups of people. Since KT is relatively safe there is no reason why it cannot be used. Whether or not KT acts as a placebo or works I ways that are yet to be understood, it has worked for a large population of people for many years in helping to get past injuries for exercise and daily life.

Questions to Consider

Have you ever used Kinesio Tape? If so, did it help alleviate pain or support movements?

[2] Patricia do Carmo Silva Parreira, Luciola da Cunha Menezes Costa, etc. (2014). Current evidence does not support the use of Kinesio Taping in clinical practice: a systematic review. Journal of Physiotherapy, 60(1), 31-39.

Stretching is a critical component of many regimens seen in clinical and fitness settings. Whether you’re a person who prefers to stretch before/after your routine, many people will attest to the physiological benefits of stretching. Proponents of stretching believe that it improves performance during exercise and prevents injuries and soreness. Some would go so far as to say that an individual may not be stretching enough when they repeatedly experience pain or injury after their workouts with no signs of improvement. Despite these enduring beliefs, the science behind the benefits of stretching is questionable. For the purposes of this blog post, we will focus on the acute, short-term effects of stretching on performance during exercise.

Three forms of stretching used in exercise and rehabilitation settings include dynamic stretching, ballistic stretching, and static stretching. Dynamic stretching is a type of stretching which involve fluid-exaggerated movements. Ballistic stretching utilizes fast countermovements. Static stretching involves extending target muscles to a limit point, and maintaining that position for an interval between 10 and 30 seconds. In order to minimize injuries, static stretching is encouraged for non-athletes.

Numerous scientific studies have shown that have shown that static stretching results in an improved joint range of motion (ROM) and greater flexibility in the muscles targeted by this technique. Conversely, research has also shown that stretching before exercises can result in a lower force output generated in the muscles that are targeted. Compliance is the lengthening of muscle fibers in response to an applied force. According to an article cited by the the National Institute of Health (Anderson, 2005), increased compliance (which occurs a result of stretching) has been linked to a decreased ability to absorb force at rest, whereas decreased compliance results in a muscle being able to withstand higher tension. This is significant because, when sarcomeres are stretched to the point that the actin and myosin filaments do not overlap, the force absorbed is transmitted to the muscle fiber cytoskeleton; resulting in fiber damage (regardless of a muscle’s joint ROM). Thus, compliance may result in decreased performance depending on the type of exercise performed. Another issue that arises related to the use of stretching before exercise is the type of stretching utilized. Science has shown that muscle fibers can experience tension when stretched as little as 20% of their total length1. Thus, it is difficult to establish a universal standard describing correct stretching techniques. In addition, improved joint ROM can be attributable to extraneous factors (such as increased pain tolerance); making the strength of its relationship to stretching highly questionable.

There are a plethora of studies conducted that attempt to quantify the effect of stretching on performance. One study, conducted by researchers at Sahmyook University in 20182 examined the effects of stretching on muscle strength, endurance, and endurance in a non-athletic sample of 13 active collegiate male students. These subjects were separated into three groups: those who did not perform any warm ups before exercise (NWU), those who performed aerobic warm ups in the form of power walking for ten minutes (AWU) before exercise, and those who performed aerobic warm ups with static stretching for ten minutes (ASU). All three groups performed isokinetic muscle testing. The stretching used in the study consisted of straddling, seated calf stretching, and standing quadriceps stretching for the lower body. Two repetitions of each stretching motion were performed for 20 sec each and the entire stretching program took 5 min to perform. All subjects rested for 1 min after warming up and then underwent isokinetic muscle testing of the knee joints. The sequence of performance of each warm-up exercise was individually randomized. In the successive weeks, each group was tested according to the type of warm-up performed. The testing was conducted for 3 weeks, and all groups were allowed a week to rest in between tests.

In order to quantify the results in each group, a knee extension/flexion isokinetic dynamometer was used. Participants were asked to extend and flex the knee by exerting their maximum strength as fast as possible while keeping their trunk up against the backrest during the test and to hold onto the handles. The subjects performed the maximal test of four repetitions. Each maximal test was conducted with an angular speed of 60°/sec to measure isokinetic muscle strength and an angular speed of 180°/sec to measure isokinetic muscle power. In addition, the muscle endurance test was conducted with an angular speed of 240°/sec. The exercise was conducted twice prior to testing to familiarize the subjects with the test, thereby achieving optimal results. The subjects were verbally encouraged and allowed to view their torque graphs during testing as a form of visual feedback to increase motivation. To analyze muscle strength, power and endurance, measurements of the left and right knee joints were divided into each independent variable before data processing was performed. In addition, psychological evaluations in the form of questionnaires were administered to subjects before and after workouts for individuals in all three groups. These assessments utilized a 5-point Likert scale (1, very bad; 2, bad; 3, average; 4, good; 5, very good). The Kruskal–Wallis rank test were used to examine the differences of variables among groups and the Wilcoxon test was used to investigate psychological conditions before and after warm-ups within times in each group. A Mann–Whitney post hoc test was implemented to detect any significant differences in the Kruskal–Wallis test. The significance of all data was established at p ≤0.05. The results from the table have been included in figures attached to this post. The data is shown in the bottom of this point via a hyperlink.

Based on the results of this experiment, the researchers concluded that there was no significant effect of the type of warm-up activity on performance in any of the tests performed in this study. Shown in Table 2, at 60°/sec (which is an angular speed for rating muscle strength), the NWU showed higher rates for both the extensor and flexor. However, the researchers determined that the difference was not statistically significant Shown in Table 3, at 180°/sec (an angular speed associated with rating muscle power), AWU and ASW groups attained higher rates for the flexor and extensor, respectively, although the difference was not statistically significant. The total work at 240°/sec (which reflects muscle endurance) was higher in ASW for both the flexor and extensor than NWU and AWU, though not statistically significantly. These results are shown in Table 4. In a similar manner to the trends seen when evaluating athletic performance, the individuals in the ASW group marked higher scores on their psychological assessments than the AWU and NWU groups. The results are shown in Table 5. However, the researchers determined that the result were not statistically significant.

Overall, while there appears to be some merit to the psychological benefits of stretching before exercising, its effect on athletic performance remains inconclusive. However, if you find that stretching helps improve your outlook/state-of-mind during the course of your workout, I would highly encourage you to continue your routine.

Questions to Consider

Based on the experiment, do you believe that stretching before a workout provides any benefits/advantages towards performance?

Does this post affect your views towards stretching?

Would you encourage someone seeking to exercise more frequently to stretch before/after their exercises?

Anyone who has partaken in any physical activity, whether it is a sport, exercise routine, or just simple around the house chores that require a little more muscle power than normal, has experienced muscle soreness or discomfort. Generally, when muscles are pushed passed what they are used to (i.e. new exercising routines, increased weight, eccentric exercises) the muscle fibers undergo damage and the body’s response is to add muscle fibers and/or to increase the size of muscle fibers to help increase muscle strength. When talking about sore muscles, it is generally thought the soreness comes from the physical effects of muscle tearing, repairing, and growing from a workout. There is, however, one part of the muscle that plays a role in not only soreness, but also range of motion (flexibility), and muscle performance that not many people know needs special attention: the myofascial tissue.

Figure 1: Skeletal muscle structure through different layers of the muscle. Myofascial tissue lies over the epimysium connective tissue which coats the muscle bundle. The epimysium, perimysium, and endomysium are specialized versions of myofascial tissue.

Different forms of fascia can be found all over the body, from encasing organs, to blood vessels and nerves, to muscle. Fascial tissue that specifically covers muscle, or myofascial tissue, is a thin, white/transparent connective tissue that covers muscle, bundles, muscle fibers, and the muscle as a whole. If you have ever picked off the thin white stuff covering parts of a chicken breast while preparing it for dinner, you tore off the myofascial tissue layer. Myofascial tissue is an extremely flexible and strong material, which is made up of elastin fibers, for stretch, and collagen fibers, for strength, that are embedded in a gelatinous ground substance, which reduces friction between the muscle fibers and promotes ease of motion [1]. Considered a “deep fascia,” myofascial tissue is made up of a more compacted weave than other fascia found throughout the body and can modify itself depending on the forces placed on it. (Figure 2). Because of this, if there is “trauma” or “injury” to the tissue, it can become out of alignment and

Figure 2: 3D visualization of myofascial tissue (white web like structure) and fascia tissue between the skin and muscle (yellow web like structure). Myofascial tissue can be related to a cotton candy structure that is extremely complex and strong. Retrieved from https://www.myofascialrelease.com/about/definition.aspx

cause trigger or dysfunctional points. These points, most commonly referred to as knots, is when the fibers that make up the tissue gets stuck together, loses its elasticity, and becomes taught [2]. Polly de Mille, R.N., C.S.C.S., director of performance services at the Hospital for Special Surgery in New York City explains in an interview for SELF that it is very similar to getting ice cream in silky smooth hair. When there are “knots” in the muscle fascia, it limits range of motion, and can trigger immune responses which can ultimately lead to pain and discomfort (cytokines have been shown to cause pain and soreness) [3,4].

Now, what is the best way to heal and prevent muscles from experiencing these knots and discomfort? When talking about getting rid of knots in your body, a massage should be the first thing that comes to mind. The “hurts so good” mentality of deep massaging muscles to where the patient feels pain and then relief afterwards is a popular desire, though not for everyone. Applying pressure and different forces to the tissue through a massage, or foam roller which we will talk about in a little bit, while moving around the fascia helps to separate and relax the tissue and muscle, allowing it to go back to its natural state. Effects also include an increase in blood flow, which should help muscles get the proper nutrients to repair. Massaging also releases “feel good” brain chemicals, like endorphins, which basically inhibit pain receptors and overall makes you feel better. A study conducted by Mal-Soon Shin and Yun-Hee Sung induced muscle fatigue on 21 young males and treated 11 of them to massages afterwards while recording surface muscle activation and position of their medial gastrocnemius muscle. According to their study, massaging increases muscle activation and strength due to a change of structural properties. However, in their discussion, they mention that not all messages are effective, which seems to be a common issue in the argument of whether foam rollers, or self myofascial release in general, works or not [5].

Massages are so great because when another person is working out your muscles, they are not only more accurate in pinpointing the location, but they can also apply more force (remember: collagen is EXTREMELY strong in ratio to its size. Proportionally, it is stronger than steel!). As great as they are, unless someone at home is a masseuse, it can be costly. Self myofascial release techniques, such as foam rolling, have taken over the exercise world and are now regularly used. Foam rolling is when the user applies pressure to “trigger point” or sore spot before or after a workout by using their body weight to roll against a foam cylinder. Though it feels good, does it actually work?

Research has proven that foam rolling is great for warming up muscles and increasing range of motion and flexibility, but the verdict is still out on decreasing muscle soreness. Though the mechanism behind foam rolling is not exactly known, there is great evidence that it does work on some type of level, whether it is physical or just simply mental. In a systematic literature review of research on using a foam roller before and after workouts, Scott W. Cheatham identified different scientific articles that were critically appraised with trusted conclusions. From these articles, he identified five studies on the effects of foam rolling and range of motion before exercising. All of these studies resulted with an increase in stretching or range in motion in test subjects [6]. It is common knowledge to stretch before a workout or game to help “warm up” the muscles so that they’re are more flexible, which helps prevent injury and soreness. It is also speculated that rolling out could create a friction that literally heats up the fascia and muscle, making it more flexible and the typical “loose” feeling [2]. After a workout, however, there is a preconception that rolling out will help with delayed onset muscle soreness and pain in general. In this literature review, Cheatham identifies two different journals that conclude that foam rolling does reduce pain, but since the mechanism behind it is still unknown, how much can we trust? In the same SELF article as mentioned previously, Lewis J. Macgregor, Ph.D., an exercise physiologist and lead author of the University of Stirling confirms foam rolling does help increase blood flow, which in turn promotes muscle recovery, but foam rolling does not actually help with myofascial release. Since the collagen in the fascia is so strong, it is argued using your body weight to roll out is not enough. Instead, the pressure of rolling stimulates nerve receptors, which sends the same “hurts so good” feeling to your brain that is then perceived as loosening up the muscle, when really it is not happening.

Overall, foam rolling and myofascial release is an effective way to warm up your muscles and stretch them out before a workout and to help stimulate more blood flow post workout, just don’t get your hopes up about avoiding soreness! Increasing range of motion and flexibility before a workout is a great step to ease muscle soreness, but foam rolling alone is not the answer. The verdict is still out on the mechanism behind the effects of myofascial release on a cellular level, but hey, if it feels good, why not!

If you’re interested, here is a video of foam rolling techniques because like anything, it’s not effective if you don’t do it properly.

In order for whole body air displacement plethysmographic machines such as the BodPod to function optimally (so that viable data can be collected), it is crucial that laminar flow is maintained throughout the machine’s ventilation system at all times. Imagine that you are an engineer (imagine that!) tasked with manufacturing the tube components for the Bod Pod.

If the flow rates in the inlet and outlet tubes are equal, the volumetric flow rate of air in the tubing system will be 0.25 cubic meters/second , and the BodPod functions in laminar/laminar-like conditions, what are the ideal dimensions for the diameters of the inlet and outlet tubes in the Bod Pod?

Assumptions

Flow rates are equal in the inlet and outlet tubes

The tubes are cylindrical

Laminar flow is maintained at all times

Pressure changes are negligible

Air circulating inside the BodPod has similar thermodynamic/kinematic properties ambient air at room temperature

Temperature conditions of the device are identical to those at room-temperature

A link has been included to a power point presentation that contains diagrams that will aid readers in solving this problem:

Figure 1: Schematic of Adult-Sized Bod Pod and circuitry components that will be used as a reference for this problem.

BACKGROUND KNOWLEDGE/ ASSUMPTIONS

According to the 4th page of the patent filed by the manufacturer, Life Instruments Inc., it is okay to assume laminar conditions inside the tubing ventilation due to the fact that flow rate inside the inlet and outlet tubes are always set to values of low magnitudes. Literature in courses such as Signals and Systems show that low flow rates result in low generation of acoustic noise by air circulation systems.

I was unsuccessful in locating some sort of testing standard that establishes set values for the volumetric flow rates of air in laminar conditions. There appears to be any information pertaining to any testing protocols the manufacturer used for design verification purposes in the original 510(k) form filed with the FDA. To establish an appropriate flow rate value for this test question, I searched for similar problems online. In short, the values for the volumetric flow rate of air (Q) ranged from 0.1 to 0.8 cubic meters/second in my searches. I decided to use a value of 0.25 cubic meters/second in this problem. By assuming that the values for Q are equal for both tubes, it is possible to design both tubes with an equal diameter. Thus, along with other reasons that will be outlined later in this section, all the solver is required to do to calculate the correct value in this problem is to use one equation.

Normally, pressure fluctuations trigger changes in tubings and pipes create flow gradients in closed ventilation systems. Because of this, mathematical expressions such a Boyle’s Law and Bernoulli’s equations are used to solve changes in volume and volumetric flow when pressure fluctuations occur. According to page 4 of the patent filed for the Bod Pod, the authors state that the use of pressure transducers which are coupled to the inlet and outlet tubes helps monitor any pressure changes that occurs in the tubing; automatically adjusting the pressure settings in the tubes to more optimal levels through negative feedback. This is done in order to maintain a constant flow rate (and thus, laminar flow throughout the circulation system). Later on in section 4 of the patent, the manufacturers also state that constant air flow can be maintained with the addition of rotary pumps to the circulation system (which are not actively displayed in any of the figures included).

The manufacturer’s statements in the patent confirm the presence of temperature-sensing circuitry in the inlet and outlet tubes that control the internal temperature of the environment inside the tubing and the pod itself. Thus, any temperature fluctuations that could create flow gradients in the device’s tubing are negligible since they are always corrected in rapid fashion. This also eliminates the need for Fourier’s law to solve the value of Q in this problem.

Assuming that the tubing is cylindrical eliminates the need to solve for any hydrodynamic radius values(which are used in equations associated with fluid flow in which tubes/pipes are any shape that is non-cylindrical).

By assuming that the air inside the device’s circulation system behaves in a similar fashion to ambient air, and that the conditions inside the circulation system are similar to those at room-temperature and that the device is used in STP conditions, it is possible to estimate the value of the kinematic viscosity of air (which is needed to solve the value for the diameter of the tubing using the Reynolds number equation along with the value of the flow rate given in the problem description and the upper-limit value of the Reynolds number associated with laminar flow).

SOLUTION

In order to solve for the value of the tube diameter, the solver must utilize the following equation:

NOTE: Pipe bore is equivalent to the diameter of the tube, and this equation is applicable to both pipe and duct installations.

First, the value of Q is already provided in the description. So the reader is already provided one unknown.

Second, the reader is told in the problem description and background section to assume laminar conditions in the circulation system. The Reynolds number value used in this problem is 2300, which is the established upper limit for laminar flow. All values at or below this number is considered laminar flow.

Third, since the reader is told to assume that the air circulating through the inlet and outlet tubes are similar in kinematic/thermodynamic behavior to ambient air at room temperature, the reader can assume that air inside the circulation system has the same kinematic viscosity as ambient air at room temperature. This value is 1.494 x 10-5 meters ^2/ second.

At this point, the only unknown that the reader is left with is the value of D, or the tube diameter. After plugging all the known values into the above-aforementioned equation and solving for the value of D algebraically, the reader should arrive at a diameter value of approximately 0.13708 meters.

Glucose and Lactate are two analytes in sweat that would be highly desirable to apply sweat sensing technology to, each for their own individual reasons. Since the biosensing technology typically used to detect these analytes utilizes enzymatic reactions, temperature of the sample being tested must be taken into consideration when interpreting results due to its effects on enzymatic activity. Therefore, temperature sensors are an essential component of any sweat sensor that aims to give reliable feedback on either/both of these analytes. Multiple temperature sensing technologies exist, but a simple, commonly used technology is resistance temperature detectors (RTDs). These simple circuits use a Wheatstone bridge with a pure metal resistor that is exposed to the sample being tested. That resistor has a temperature-dependent resistance, and its resistance affects the voltage output of the Wheatstone bridge. In order to calibrate your sensor (a necessary process to ensure it gives accurate results), you must be able to use voltage outputs of known temperatures to identify the relationship between voltage and temperature. This problem will help us learn to do so.

Problem Statement

The Wheatstone bridge shown below (figure 2.) has four resistors, three of equal resistance R=10Ω and one temperature-varying platinum resistor RT. A voltage VE=1V is provided to the system by a battery as shown. Vo is defined as the voltage difference between points a and b, and is given by the general Wheatstone bridge equation provided below (figure 1.). Resistance RT is given by RT = R0(1+α(T-T0), where α is the temperature coefficient of platinum, α= 0.00385/°C. Given that R0= 10Ω and T0=0°C…

a. Write an equation for Vo in terms of T

b. Find Vo at T=20°C, T=30°C, and T=40°C

c. Devices aren’t always exact. Your RTD is giving values of Vo(20)=19.0mV, Vo(30)=28.3mV, and Vo(40)=37.2mV. Plot these values and find a line of best fit for your RTD (assuming linear relationship*)

d. Find the voltage Vo that would be expected at T=37°C

Figure 1. Wheatstone bridge equation

Figure 2. RTD setup

*Assumptions:

Linear relationship between Vo and T- RTDs display much more linear behavior than thermocouples. They are not exactly linear, but for the purposes of this problem and learning how to calibrate, it is a fair assumption. It will cause the most error in the middle of our range of estimation, due to the parabolic nonlinearity of the true relationship between Vo and T. [1]

Solution

Figure 3. The written solutions for a, b, and d

Figure 4. Plot for part c

The algebra for solutions to parts a, b, and d of the problem are provided in figure 3. The plot for part c, created in Excel, is provided in figure 4. This plot was created by creating a column of temperature data and a column of the corresponding voltage data given in the problem statement for part c, highlighting those two columns, and creating a scatter plot. A line of best fit was added to the plot, and the equation for the line was displayed on the graph itself. Excel makes linear approximations for data sets like these very easy. While the linear approximation may not be the best fit for our data set, it appears to be very accurate, with an R2 value of 0.9998. Our final answer for Vo at 37°C makes sense, given that 34.45mV is between the values for 30°C and 40°C, 28.3mV and 37.2mV, respectively, and closer to that of 40°C. The linear approximation we made is a limitation of this solution. For a sweat sensing technology that gives medically relevant feedback to the user, we would want our analyte sensing results to be as accurate as possible, which would involve a curve-fitting technique as opposed to a linear approximation for our RTD. With the linear calibration we performed, we could use the values of Vo received from our RTD to determine the temperature of samples between 20-40°C with a pretty high level of accuracy.

Wrist pedometers are used by many to count their steps, and notify users when they “reach their 10,000”. These wearable devices quantify step activity and give indiviudals an idea of exactly how much they are moving throughout the day.

Accelerometers are often used within these wearable devices to detect the force acting on the device. The force acting on the accelerometer is correlated to an analog voltage output, which must be processed through a series of op amps to turn a users movement into an electrical output that can be analyzed through signal processing, but what signal processing circuitry is needed following the accelerometer within a wrist pedometer to correlate force acting on the pedometer to steps taken by the user?

In this post we will solve at the following engineering problem associated with pedometers: what signal processing circuitry is needed to convert the analog voltage input from an accelerometer to a binary digital signal that can be correlated to steps taken by a user?

Background

Figure 1. Force acting on wrist pedometer during gait cycle[1].

The average person takes between 0 and 120 steps per a minute. Throughout each gait cycle, a wrist pedometer experiences forces relative to its position, as shown in Figure 1. While standing the force detected by the pedometer is 1G (one times the force of gravity). When a user is pushing against the ground to step forward the force detected by the pedometer can rise above 1G, and while the user is between steps the force detected by the pedometer can go below 1G. The pedometer can detect when a user takes a step by monitoring forces and determining when the 1G threshold is crossed. Many wrist pedometers use a threshold of at least +/- 0.2G to prevent noise and standing movements from being accounted for in step count. So a step count will be equal to crossing the 1.2G and -1.2G thresholds[1].

Accelerometers are often used to relate the force acting on an object to an electrical signal. Analog Devices, a circuitry component manufacturer, produces an +/- 2g accelerometer that relates forces between -2g and +2g to a voltage output, as shown in Figure 2. A linear region exists between +/- 2g, which can be defined by the following simplified function V(g)=(.875*g)+2.5 [2].

Approach

In designing the signal processing circuitry necessary to convert an analog signal from an accelerometer to a binary digital signal, we will do the following:

1.Define the input signal in terms of force acting on a wrist pedometer, and the voltage output of an accelerometer

4.Use LTSpice to model desired circuitry, and confirm that designed circuit solves the defined engineering problem

Signal Input

It is known that the force acting on a wrist pedometer can be defined by a sine wave function fluctuating +/ 0.5g around 1g, with a frequency of 0-2Hz. Therefore we will define the force acting on the pedometer as F(t)= 0.5sin(t) + 1g. Given the voltage output of analog devices accelerometer is V(g)=(.875*g)+2.5, the voltage output of the accelerometer can be defined as V(t)=0.4105sin(t)+3.375.

First, the input signal should be passed through a low pass filter, with a cutoff frequency of 2Hz to remove high frequency noise from the signal. The force acting on the pedometer, and voltage output of an accelerometer can be defined by sine wave functions. The baseline of accelerometer voltage output exists above zero volts, therefore a subtractor should be used to bring the baseline of this signal to 0V. A full wave rectifier will be used as an AC to DC converter, converting both polarities of the signal to a pulsating DC signal. A compactor will be used to produce a binary DC output that indicates whether the signal is above a given threshold, voltage relative to passing +/- 0.2g force threshold. This binary signal is the system output and can be used to count total steps taken by a user.

Circuit Components

Circuit components were selected to complete necessary signal processing, and assumed to be ideal for simplification of solving this problem.

Low pass filter

Figure 6. Low pass filter

With a cutoff frequency of 2Hz, a low pass filter with a Capacitor of 4.7 nF and resistor of 0.0169 Ohms can be used to filter out high frequency noise

Follower

Figure 7. Op amp acting as follower

Follower used to preserve signal and prevent current flow back to the user

Subtractor

Figure 8. Op amp acting as a subtractor

A subtractor can be used to reduce the baseline signal to zero. Given our voltage input is V(t)=0.4105sin(t)+3.375 V, and the Voltage output of this component is Vout = (R3/R1)*(Vin-Vs), we will set Vs=3.375V DC and R1=R2=R3=100 Ohm to bring the baseline signal down to 0V.

Full Wave Rectifier

Figure 9. Op amps acting as a full wave rectifier

A full wave rectifier will be used to convert all polarities of the input signal to the same polarities. If R1=R2=R3=R4=R5, then if Vin>0 Vout=Vin and Vin<0 Vout=-Vin. Therefore, we will set all the resistors equal to each other to achieve a rectified DC signal.

Comparator

Figure 10. Op Amp acting as a comparator

A comparator will be used to convert the pulsating DC signal to a binary digital output. Op amps functioning as comparators follow the rule that if V+>V- Vout = Vc+ and V->V+ Vout=Vc-. In our ideal circuit, we aim our binary signal to be either 0 or 1.

V+ terminal will be our signal, and we look to determine if this signal represents crossing the 1.2g threshold. To find what the V- terminal should be we need to determine the voltage at this point in the circuit if it has crossed the threshold. Given, V(g)=(.875*g)+2.5, V(g=1.2)=3.52. The signal is brought through a subtractor where it is reduced by 3.375 and afterword is no longer amplified or modified, so the threshold voltage at this point is 0.1534 V. The negative input terminal will be set to be a DC voltage of 0.1534V.

To generate a binary output where 0V= not crossing the threshold and 1V= crossing threshold, the op amp terminals will be set to be Vc+ = 1V and Vc-=0V.

LTSpice was used to model the designed circuit, as shown in figure 11. This circuit was simulated using LTSpice software and it’s ability to produce a binary digital output from an analog signal was verified as depicted in figure 12.

A series of signal processing components were integrated within a circuit, depicted in figure 13, to convert an analog voltage signal from an accelerometer into a binary digital signal. This circuit removes high frequency signal noise, reduces the signal baseline, generates a pulsating DC signal, and generates a binary signal output, as shown in figure 14.

This binary digital output can be correlated to steps taken, as two square waves is equal to one step taken. These square waves can be counted by an integrated software and used to count user steps. Thus, turning the analog accelerometer voltage output into a binary digital signal.

This binary signal can be used to count steps and step frequency, and when integrated with GPS and other technologies can be used to determine step distance and user speed.

With one two sqaure waves equaling a step, the designed integrated circuit turns user movement into step count, enabling the signal processing necessary to count those 10,000 steps everyone is so desperately trying to reach!

An 18-year-old, 5’4”, 130 lbs female soccer player is just recovering from an ACL tear and wants to know if she can get back in the game. She has been super cautious and tentative to rehab strength exercising routines, so she is sure she is ready, but wants to quantify her strength. To do this, she decides to measure her quadricep and hamstring strength on an isokinetic dynamometer and evaluate her hamstring to quad ratio, which should be between 50 and 80 percent [1]. Other important values include power, work, and peak force to assess the muscle and plan for future rehab exercise routines.

Based on previous studies, to test for power and strength of a muscle, the optimal speed is 60º/sec [2]. She also performs the test with a range of 0-90 º. The results of her hamstring force came back as 54.663 lbs and her recorded quadricep torque value determined by the isokinetic dynamometer is 102.45 lbs*ft3. The patient also wants to know her kick velocity (for fun). The computer is not properly calculating important values, and hand calculations must be performed to ensure accuracy. Calculate the power, work, and force of the quadricep, the angular speed at which the leg kicks, and the hamstring to quadricep ratio to determine if the patient can go back to playing.

Solution:
Assumptions: To simplify the math, we are ignoring the effects of gravity and inertia from the swinging limb. In real life, they play a major part in the force read by the machine and there are algorithms the computer goes through to factor out the effects. Also, the math that is performed based on the free body diagram is the forces on the knee joint, not just the quadricep. There are many forces that play a part, but for simplicity reasons we will treat them as only the force produced by the quadricep. Furthermore, there are other considerations when thinking about ACL recovery such as muscle strength and also whether or not the muscles are even. In this problem, we only look at one muscle and do not do a comparison.

1.Since Torque is given (102.45 lbs*ft), Force can be found by

Torque=〖Force〗_quad x d or 〖Force〗_quad*d_perpendicular
First: find perpendicular distance, which will be the length from the patient’s knee to ankle (d on free body diagram)
From the anthropometric table, the distance is Height*(0.285-0.039), where H= 5.33 ft.
Therefore. d=1.312 ft

102.45 lb*ft=〖Force〗_quad*1.312ft
〖Force〗_quad=78.09 lbs

2.Now that Force of the quadricep is found, we can solve for work

The distance, in this case, is the distance the leg travels, which will be the arch distance
s (arch distance)=rθ
r in this case is equal to d. Also, the range (θ) is 90 º, which in radians is 1.571 (90*(π/180))
s=(1.312)(1.571)= 2.06 ft
Now that we have d, multiply by force to get work
Work=78.09 lbs*2.06 ft=160.96 ft*lbs

4.To find angular velocity (ω) her leg is going, the angular acceleration must be determined based off of the force exerted by the quadricep

The following equations must be used
F=m_lowerleg*a_n
a_n=ω^2 r,where r=d
*Note: Since there is a circular motion, angular acceleration must be assessed. Since there is a constant velocity, there is no at component.

Using the weight chart, you should find the weight of the lower leg is 0.0618*weight, which in this case is

When designing a portable Near-Infrared Spectroscopy (NIRS) device for the measurement of muscle oxygenation, design engineers have plenty of factors to consider. They must think about battery life, portability, affordability, safety, and many other design criteria. Before considering many of these criteria, however, an engineer must design a working technology that is capable of actually measuring muscle oxygenation. Without this basic attribute, the device would be a complete failure. The basics for measurement of relative oxygenated and deoxygenated hemoglobin concentrations was introduced previously in the patent blog post, but the engineering design problem was mostly glossed over. This post will dive a little deeper into the quantitative nature of measurement of muscle oxygenation and what functions the design engineer must consider when designing a device that will operate properly and accurately. The main question to be answered is: how does an engineer use light to measure concentration of a particle in muscle?

As mentioned before, NIRS works by measuring the absorbance or attenuation of light as it passes through a sample to make a measurement of concentration of the absorbing analyte or particle. Also previously introduced were the benefits of using near-infrared light since it can pass through biological tissue and is primarily absorbed by hemoglobin. In an ideal world the absorbance is defined by the Beer-Lambert Law. According to this law, the absorbance of a particle is equal to the natural log of incident light over the detected light and this is further equal to the product of the molar absorbance coefficient, the concentration of the particle, and the mean path length of detected photons. In an ideal case this law works because it describes when light is shown through a glass cuvette with a solution with only one absorbance particle, but this is not helpful for a NIRS device for muscle oxygenation. Thus, for a NIRS device, the modified Beer-Lambert Law must be used, which is the same as the original equation but with an extra scattering term to account for photon scatter when passing through tissue like skin and muscle (Eqn. 1).

Here A is absorbance, I0 is incident (transmitted) light, I is detected light, ɛ is molar absorbance coefficient, c is concentration, L is mean path length, and G is the scattering term. This is great in theory because it appears that concentration can be calculated relatively easily, but there are further problems to solve. Start by considering the knowns and unknowns. The absorbance coefficient is a known value for any analyte given the wavelength of the laser used (Fig. 1), and the path length can easily be found from the distance between the light emitter and detector with some regards to the path shape which is known to be roughly banana shaped. This leaves two unknown terms: the unknown that to be measured, i.e. concentration, and the scatter term. The scatter term is unfortunately a problem. It varies by tissue and considering the device should be designed for consumers to use on different locations, different muscles, and different amounts of say fat that may lie in the way of the muscle, this G term will forever be changing. Thus, there needs to be a way to get rid of it. The easiest way to do this is to find change in absorbance so that G will be subtracted away. This uses the assumption that G is constant for a given location. The resulting equation will then give change in concentration as it is the only factor that changed between measurements 1 and 2 (usually an initial measurement and a second measure at a later time) (Eqn. 2). Notice that absorbance is now equal to the natural log of the first intensity detected divided by the second intensity measured based on the identity (log(x/y) = log(x)-log(y). Note that the need to get rid of G, because it cannot be calculated on every single consumer, leads to the fact that NIRS devices almost always measure change in concentration or relative concentration when measuring muscle oxygenation.

This equation looks great. So change in concentration as opposed to exact concentration is found, but so what, this is still a very helpful measure for oxygenation during exercise. BUT, this equation is not the whole story. NIRS works by measuring both oxygenated and deoxygenated hemoglobin (Hb). Both species of Hb contribute to absorbance in the near-infrared range. Thus the equation actually looks like this (Eqn. 3)

In this equation, subscript O is used for oxygenated Hb, and subscript Hb is used for deoxygenated Hb. Now there are two unknowns and only one equation. So what does a smart engineer do? They add more lights. By measuring multiple wavelengths, two changes in absorbance can be measured allowing both concentrations to be calculated by solving the system of equation (Eqn. 4-5).

In these equations, superscripts refer to the wavelengths of light 1 and 2. It must be remembered that absorbance coefficient, absorbance change, and path length will all vary based on wavelength. This clearly allows for the output of relative concentrations or total blood oxygen saturation percentage (oxyHb / [oxyHb + deoxyHb]). Here the assumption is that total Hb is equal to oxyHb plus deoxyHb. The last piece of the puzzle for an engineer is to decide on what wavelengths should be used for the lights. This is a very impactful decision in building the algorithm to calculate the outcome measures of the device since ɛ, A, and L all depend on wavelength. It should be noted based on Figure 1 that certain wavelengths will be better than others. For example, if 805 nm light is used, then the absorbance coefficients for both species of Hb will be the same. This leads to irrational answers for Equations 4 and 5, so this wavelength should be avoided. The best case is to pick a wavelength above and below this so that one is more sensitive to oxyHb and the other is more sensitive to deoxyHb. Thus, using 750 and 850nm could be viable options, and these are used in several current devices.

These results allow an engineer to design a device that will properly measure muscle oxygenation through the relative concentrations of oxygenated and deoxygenated Hb. A reminder that some of the assumptions that needed to be made were that the tissue was homogenous, that oxy and deoxy Hb are the only particles contributing to absorbance, that absorbance is constant in time when Hb concentrations do not change, that the scattering term remained constant, and that oxy + deoxy Hb is the total Hb. Realistically, tissue is not homogeneous, but this assumption causes smaller errors in the volumes being considered close to the skin surface. Unfortunately, Hb is not the only chromophore contributing to absorbance. Fat is a major problem because it shares a similar range of wavelengths for absorbance. Some devices take fat correction into account, but other do not, and papers have pointed this out. It is reasonable to assume that absorbance is constant in time when concentration is constant, but pulsatile flow can cause error here. The scattering term should remain constant if the position of the device is not changed, and it is also reasonable to assume that there are not Hb species besides oxy and deoxy in the muscle. Some of these do cause limitations to the design described here, and as already mentioned it will only measure change in concentration not the absolute value. In conclusion, two wavelengths of light are needed measure muscle oxygenation with NIRS.

Identify:

Heart rate measurements are a very versatile and useful tool for both starting and veteran athletes. Among many other uses [1], it can be used as a general gauge of how hard you are working out at that moment, and it can help determine improvement as your max heart rate increases. But putting a hand to your chest and counting the beats per minute is an impractical way to measure heart rate. So to help us measure this useful metric, we have heart rate monitors that can take our heart rate for us.

On the market, there are two types of heart rate monitors: Chest-strap monitors and wrist-strap monitors. Most people who aren’t even athletes probably have a wearable that can monitor heartbeats. Even most modern phones have the ability to measure your heart beats. However, despite their ubiquity, they have one major downfall: Wrist-strap monitors simply aren’t incredibly accurate. Besides the point of location, the wrist has several different factors [2] that make it difficult to get a good reading, ranging from skin-tone to motion. All of these factors produce noise that helps to muddy the results and can produce odd and inaccurate readings. To ensure we get the most accurate results to accurately determine our exercise maximum, it is this noise that we must turn to curb. But how do we go about reducing noise?

Formulate:

Modern wearable HRMs use a technology called photoplethysmography or PPG. In essence [3], the device shines a light through a bulb (usually an LED), that passes through the skin and muscles. A majority of this light will be absorbed by the surrounding skin and muscles. The blood absorbs the light that does make it through, which is the crux. By measuring the amount of light that is absorbed, the device can pick up on pulses in the blood based upon the differences in these absorbances. This technology is very similar to how spectrophotometers work, with both measuring the absorbance that a material has. But unlike a spectrophotometer which measures the absorbance through the material, PPG measures constantly, listening in for very small changes in absorbance that can be used to determine heart rate.

An example of PPG. Pulses within the vessel cause even more light to be absorbed than would normally. This is what the wearable is measuring.

PPG is very sensitive to physical sensations like bumps and pumps, which produces noise. When the sensor is jostled due to motion, the small amount of signal that is recorded gets muddled, which produces the majority of the noise that we are trying to cut down. This noise can cause very odd results, such as heart rates that vary wildly [4]. The noise is not present while not in motion, but for athletes who want to know how high their heart rate can get, this is not acceptable. As noise caused by motion is the leading cause of these very odd discrepancies in heart rate, we need to lower it as much as possible.

In order to solve this, we are going to separate the signals read between three metrics: a DC, an AC, and a noise component. We shall be ignoring noise caused by the optical signal, as it is subtracted by the sensor through the use of ambient light measurements [5]. Thus, the incoming current that is read can be simplified as:

Incoming Current = DC component + AC component + Noise

The DC component of the signal comes from changes in respiration in the vessel, while the AC component comes from variation in blood volume due to the heartbeat.

Solve:

If we want to reduce the amount of noise, we are going to have to pass the incoming signal through a filter. When the signal comes back to the wearable, it must interpret the signal, from raw absorbance values to electrical signals that are then interpreted by the wearable. And since we assume that optical light noise is negligible, we can focus on removing noise due to motion. Using biophysical-signal characterization techniques [6] as our filter, we can compare the incoming signal, and remove noise caused by motion. The remaining non-noise components will have to be amplified in order to get a complete, accurate signal. We do this in order to fill in the gaps made when we remove several points of noisy data.

By using a current filter, we hope to minimize the amount of noise that is detected alongside the heart rate of the monitor. If we can eliminate the noise read alongside the signal, we can get more accurate results, as the signal interpreted would consist only of the AC and DC components. However, this approach focuses only on noise made by motion. As stated before, there are several different sources of noise that interfere with accurate measurements. While motion is one of the primary sources of noise, other factors like skin tone, gaps between the sensor and the skin, and the location of the sensor can introduce more noise. This solution also has the possibility of cutting off accurate readings that are interpreted by the sensor as noise. Athletes who do a lot of vigorous exercises may find that their heart rates are inaccurate under this solution if their heart rates spike hard enough during exercise.

It is common for people worry about their Body Mass Index (BMI) values after visiting the doctor’s office. What many people don’t know is that these BMI values do not take into account what body weight comes from muscle and what comes from fat. This can be hard for individuals who contain high amounts of muscle, which weighs more than fat, and get a BMI value back saying that they are overweight.

One way to differentiate between an individual’s fat free mass (FFM) and their fat mass (
FM) is by using a bioelectrical impedance analyzer. These analyzers work by sending a low electrical current through the body from one electrode to another. This electrical current will pass quickly through hydrated tissues such as muscle and slowly through low hydrated tissues like fat.

There are many different factors to be taken into consideration when programming a bioelectrical impedance analyzer as shown above. Many estimated values for these analyzers come from average values and standard deviations of measurements from more accurate body composition tests such as hydrostatic weighing or Dual-energy X-ray absorptiometry (DXA). Specific equations based off of these values must be input into the system that will be able to give back estimates of an individual’s specific body composition given an input of the individuals weight, height, and gender. The problem with these analyzers is that the estimated values don’t accurately or even closely relate to each individual.

Formulate

For a bioelectrical impedance analyzer, the impedance value is mathematically found from the equation Z^2 = R^2 + Xc^2. Within this equation Z is the impedance, R is the resistance, and Xc is the reactance. The resistance is the opposition of a conductor to the alternating current and the reactance is the additional opposition to the current from the storage effects of the cell membranes and tissue interfaces.

As an engineer it is important to find the right programming equations for the technology being made. These equations will vary in accuracy depending on the sex and ethnicity of its user. After the impedance has been calculated from the electrical current, it will need to be plugged into an equation, along with height, weight, and gender to find fat mass. When using segmental analyzers each different segment being measured will use its own specific equations for FM and the segments will then be summed for a total body FM. A typical FM equation for a non-segmental analyzer for ages 16-80 may be set up as:

FM(kg) = C1 + C2 Age + W + C3 (H(m)^2 / Z) – C4 H(m)

Where H(m) is height in meters, W is weight kg, Age is age in years, Z is from the previous equation depending of the testing frequency and each C variable is a different constant. The constant values will be determined using linear regression models of data taken on a group of individuals using a different form of body composition analysis.

The following assumptions can be made when programming the equations:

The electrical current follows the path of least resistance within the body

Both the body and its specified segments follow a cylindrical ‘typical’ shape

If these two assumptions hold true and the following equations are programmed correctly an FM estimate can accurately be made.

Solve

The following measurements and calculations will then be made for fat mass:

Z^2 = R^2 + Xc^2

FM(kg) = C1 + C2 Age + W + C3 (H(m)^2 / Z) – C4 H(m)

Using the standard deviations as C values from data taken from a previous body composition study in Japanese women [1],the following equation can be determined:

FM(kg) = 37.91 + 18 Age + W + 0.6144 (H(m)^2 / Z) – 6.7 H(m)

Using these calculations along with a weight measurement from a scale an individual can then accurately assess their body composition health and fat free mass rather than using the BMI percentile chart.

Weight = FFM + FM

FFM = Weight – FM

It is important to understand that this developed equation will be limited only to Japanese females. If a scale programmed to find fat mass using this equation was used by a male, even a Japanese male, they would get an inaccurate reading. These reading will be inaccurate mainly due to the differences in how each sex and different ethnicities hold water within their body. This equation found for a BIA scale would be reasonable for female Japanese users only. In order for the scale to be reasonable for other individuals the programmed equation will need to be changed based of previous body composition findings of other groups based on ethnicity and sex.